function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta
result = sigmoid(X*theta);
J = (-1 * (sum((y .* log(result)) + ((1-y) .* log(1-result)))/m)) + sum(theta(2:size(theta),1) .^ 2)*(lambda/(2*m));

grad = ((X' * (result - y))+(lambda * theta))/m;
grad(1) = grad(1) - ((lambda * theta(1))/m); 




% =============================================================

end
